Problem: $P(x)$ is a polynomial. Here are a few values of $P(x)$. $P(-2)=1$ $P(-1)=3$ $P(1)=0$ $P(2)=4$ What is the remainder when $P(x)$ is divided by $(x-1)$ ?
Explanation: We can use the polynomial remainder theorem to solve this problem: For a polynomial $p(x)$ and a number $a$, the remainder on division by $x-a$ is $p(a)$. According to the theorem, the remainder when $P(x)$ is divided by $(x-{1})$ is $P({1})$, and we are given that $P({1})=0$. In a similar manner, the remainder when $P(x)$ is divided by $(x+2)$, which can be rewritten as $(x-({-2}))$, is $P({-2})$, and we are given that $P({-2})=1$. In conclusion, The remainder when $P(x)$ is divided by $(x-1)$ is $0$. The remainder when $P(x)$ is divided by $(x+2)$ is $1$.